{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian Data Analysis, 3rd ed\n",
    "##  Chapter 10, demo 3\n",
    "\n",
    "Normal approximaton for Bioassay model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import arviz as az\n",
    "import numpy as np\n",
    "from scipy.optimize import minimize\n",
    "from scipy.stats import gaussian_kde\n",
    "import preliz as pz\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "pz.style.use('preliz-doc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Bioassay data, (BDA3 page 86)\n",
    "x = np.array([-0.86, -0.30, -0.05, 0.73])\n",
    "n = np.array([5, 5, 5, 5])\n",
    "y = np.array([0, 1, 3, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the posterior density in grid\n",
    "#  - usually should be computed in logarithms!\n",
    "#  - with alternative prior, check that range and spacing of A and B\n",
    "#    are sensible\n",
    "ngrid = 100\n",
    "A = np.linspace(-4, 8, ngrid)\n",
    "B = np.linspace(-10, 40, ngrid)\n",
    "ilogit_abx = 1 / (np.exp(-(A[:,None] + B[:,None,None] * x)) + 1)\n",
    "p = np.prod(ilogit_abx**y * (1 - ilogit_abx)**(n - y), axis=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sample from the grid\n",
    "nsamp = 1000\n",
    "samp_indices = np.unravel_index(\n",
    "    np.random.choice(p.size, size=nsamp, p=p.ravel()/np.sum(p)),\n",
    "    p.shape\n",
    ")\n",
    "samp_A = A[samp_indices[1]]\n",
    "samp_B = B[samp_indices[0]]\n",
    "# add random jitter, see BDA3 p. 76\n",
    "samp_A += (np.random.rand(nsamp) - 0.5) * (A[1]-A[0])\n",
    "samp_B += (np.random.rand(nsamp) - 0.5) * (B[1]-B[0])\n",
    "\n",
    "# samples of LD50\n",
    "samp_ld50 = -samp_A / samp_B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the mode by minimising negative log posterior. Compute gradients and Hessian analytically, and use Newton's method for optimisation. You may use optimisation routines below for checking your results. See help for scipy.optimize.minimize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the optimised function\n",
    "def bioassayfun(w):\n",
    "    a = w[0]\n",
    "    b = w[1]\n",
    "    et = np.exp(a + b * x)\n",
    "    z = et / (1 + et)\n",
    "    e = - np.sum(y * np.log(z) + (n - y) * np.log(1 - z))\n",
    "    return e\n",
    "# initial guess\n",
    "w0 = np.array([0.0, 0.0])\n",
    "# optimise\n",
    "optim_res = minimize(bioassayfun, w0)\n",
    "# extract desired results\n",
    "w = optim_res['x']\n",
    "S = optim_res['hess_inv']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the normal approximation density in grid. Note tha this is just for the illustration and in real case we would not need to evaluate this, and we would only use the draws from the normal distribution approaximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Construct a grid array of shape (ngrid, ngrid, 2) from A and B. Although\n",
    "# Numpy's concatenation functions do not support broadcasting, a clever trick\n",
    "# can be applied to overcome this without unnecessary memory copies\n",
    "# (see Numpy's documentation for strides for more information):\n",
    "A_broadcasted = np.lib.stride_tricks.as_strided(\n",
    "    A, shape=(ngrid,ngrid), strides=(0, A.strides[0]))\n",
    "B_broadcasted = np.lib.stride_tricks.as_strided(\n",
    "    B, shape=(ngrid,ngrid), strides=(B.strides[0], 0))\n",
    "grid = np.dstack((A_broadcasted, B_broadcasted))\n",
    "dist = pz.MvNormal(w, S)\n",
    "p_norm = dist.pdf(x=grid)\n",
    "\n",
    "# draw samples from the distribution\n",
    "samp_norm = dist.rvs(size=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute Pareto smoothed importance sampling weights and Pareto diagnostic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pareto khat is 0.66\n"
     ]
    }
   ],
   "source": [
    "lg = np.log(dist.pdf(samp_norm))\n",
    "Ar = samp_norm[:,0]\n",
    "Br = samp_norm[:,1]\n",
    "ilogit_abx = 1 / (np.exp(-(Ar[:,None] + Br[:,None] * x)) + 1)\n",
    "lp = np.sum(np.log(ilogit_abx**y * (1 - ilogit_abx)**(n - y)), axis=1)\n",
    "lw = lp - lg\n",
    "lw, pk = az.stats.psislw(lw)\n",
    "print(\"Pareto khat is {:.2}\".format(pk))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Importance sampling weights could be used to weight different expectations directly, but for visualisation and easy computation of LD50 histogram, we use resampling importance sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# resampling importance sampling\n",
    "pis = np.exp(lw)\n",
    "nsamp = 1000\n",
    "samp_indices = np.random.choice(pis.size, size=nsamp, p=pis)\n",
    "rissamp_A = Ar[samp_indices]\n",
    "rissamp_B = Br[samp_indices]\n",
    "# add random jitter, see BDA3 p. 76\n",
    "rissamp_A += (np.random.rand(nsamp) - 0.5) * (A[1]-A[0])\n",
    "rissamp_B += (np.random.rand(nsamp) - 0.5) * (B[1]-B[0])\n",
    "\n",
    "# samples of LD50\n",
    "rissamp_ld50 = - rissamp_A / rissamp_B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create figure with all results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x1000 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert samples to InferenceData objects\n",
    "samples = az.from_dict({\"A\": samp_A, \"B\": samp_B})\n",
    "samples_norm = az.from_dict({\"A\": samp_norm[:, 0], \"B\": samp_norm[:, 1]})\n",
    "rissamples = az.from_dict({\"A\": rissamp_A, \"B\": rissamp_B})\n",
    "\n",
    "fig, axes = plt.subplots(3, 3, figsize=(13, 10))\n",
    "axes = axes.reshape(3, 3)\n",
    "\n",
    "# Common axis limits and ticks\n",
    "xlim, ylim = (-2, 6), (-5, 30)\n",
    "yticks = np.linspace(0, 30, 4)\n",
    "ld50_xlim, ld50_xticks = (-0.8, 0.8), np.linspace(-0.5, 0.5, 3)\n",
    "\n",
    "# Row 0: True posterior\n",
    "axes[0, 0].imshow(p, origin=\"lower\", aspect=\"auto\", extent=(A[0], A[-1], B[0], B[-1]))\n",
    "axes[0, 0].set(xlim=xlim, ylim=ylim, xlabel=r'$\\alpha$', ylabel=r'$\\beta$', yticks=yticks)\n",
    "\n",
    "az.plot_pair(samples, marginals=False, ax=axes[0, 1])\n",
    "axes[0, 1].set(xlim=xlim, ylim=ylim, xlabel=r'$\\alpha$', ylabel=r'$\\beta$', yticks=yticks)\n",
    "axes[0, 1].text(0, -2, f\"p(beta>0)={np.mean(samp_B > 0):.2f}\")\n",
    "\n",
    "az.plot_posterior(samp_ld50, kind=\"hist\", point_estimate=None, hdi_prob=\"hide\", ax=axes[0, 2])\n",
    "axes[0, 2].set(xlim=ld50_xlim, xlabel=r'LD50 = -$\\alpha/\\beta$', yticks=[], xticks=ld50_xticks, title=\"\")\n",
    "\n",
    "# Row 1: Normal approximation\n",
    "axes[1, 0].imshow(p_norm, origin=\"lower\", aspect=\"auto\", extent=(A[0], A[-1], B[0], B[-1]))\n",
    "axes[1, 0].set(xlim=xlim, ylim=ylim, xlabel=r'$\\alpha$', ylabel=r'$\\beta$', yticks=yticks)\n",
    "\n",
    "az.plot_pair(samples_norm, marginals=False, ax=axes[1, 1])\n",
    "axes[1, 1].set(xlim=xlim, ylim=ylim, xlabel=r'$\\alpha$', ylabel=r'$\\beta$', yticks=yticks)\n",
    "axes[1, 1].text(0, -2, f\"p(beta>0)={np.mean(samp_norm[:, 1] > 0):.2f}\")\n",
    "\n",
    "bpi = samp_norm[:, 1] > 0\n",
    "samp_ld50_norm = -samp_norm[bpi, 0] / samp_norm[bpi, 1]\n",
    "az.plot_posterior(samp_ld50_norm, kind=\"hist\", point_estimate=None, hdi_prob=\"hide\", ax=axes[1, 2])\n",
    "axes[1, 2].set(xlim=ld50_xlim, xlabel=r'LD50 = -$\\alpha/\\beta$', yticks=[], xticks=ld50_xticks, title=\"\")\n",
    "\n",
    "# Row 2: Importance sampling\n",
    "axes[2, 0].axis(\"off\")\n",
    "\n",
    "az.plot_pair(rissamples, marginals=False, ax=axes[2, 1])\n",
    "axes[2, 1].set(xlim=xlim, ylim=ylim, xlabel=r'$\\alpha$', ylabel=r'$\\beta$', yticks=yticks)\n",
    "axes[2, 1].text(0, -2, f\"p(beta>0)={np.mean(rissamp_B > 0):.2f}\")\n",
    "\n",
    "az.plot_posterior(rissamp_ld50, kind=\"hist\", point_estimate=None, hdi_prob=\"hide\", ax=axes[2, 2])\n",
    "axes[2, 2].set(xlim=ld50_xlim, xlabel=r'LD50 = -$\\alpha/\\beta$', yticks=[], xticks=ld50_xticks, title=\"\");\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that normal approximation centered at the posterior mode is able to catch some of the posterior shape, but the gives much larger value for $p(\\beta>0)$ and longer tails for the marginal posterior of LD50. The importance sampling is able to partially correct the normal approaximation, although it's clearly missing part of the mass in long tail of the true distribution, but still we get much improved approximation for the marginal posterior of LD50."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "bda_py_demos",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
